The papers most related to our work is that by [1]} and [2]}. [1]} considered arms with the highest mean-variance to be optimal, and their definitions and methods can be analogously defined for minimising the mean-variance. [2]} defined arms with the minimum CVaR as optimal in their “infeasible instance”, which produced theoretical analogues for “feasible instances”. This hints that the heavy duty analysis happens in trying to choose arms with the risk measure minimised. Our paper seeks to explore the efficacy of Thompson sampling in the analogous risk-minimising problem setting proposed by [1]}, but instead considering the entropic risk measure. We demonstrate and prove the asymptotic optimality of ERTS, whose asymptotic upper bound matches the theoretical lower bound for consistent algorithms that solve the entropic risk MAB for Gaussian bandits.
